Abstract
In this paper, a three-order Taylor-type numerical differentiation formula is firstly utilized to linearize and discretize constrained conditions of model predictive control (MPC), which can be generalized from lower limb rehabilitation robots. Meanwhile, a new numerical approach that projected an active set conjugate gradient approach is proposed, analyzed, and investigated to solve MPC. This numerical approach not only incorporates both the active set and conjugate gradient approach but also utilizes a projective operator, which can guarantee that the equality constraints are always satisfied. Furthermore, rigorous proof of feasibility and global convergence also shows that the proposed approach can effectively solve MPC with equality and bound constraints. Finally, an echo state network (ESN) is established in simulations to realize intention recognition for human–machine interactive control and active rehabilitation training of lower-limb rehabilitation robots; simulation results are also reported and analyzed to substantiate that ESN can accurately identify motion intention, and the projected active set conjugate gradient approach is feasible and effective for lower-limb rehabilitation robot of MPC with passive and active rehabilitation training. This approach also ensures computational when disturbed by uncertainties in system.
Highlights
The number of limb impairment patients who were injured by stroke has increased year by year, and this disease has been developing in the direction of youth, seriously endangering the health of patients (Zorowitz et al, 2013)
Combining the echo state network (ESN) model and intention recognition, the model predictive control (MPC) and projected active set HS-type conjugate gradient algorithm (PASHS) algorithm are utilized to active rehabilitation training
Where q, q, q ∈ R2 are angle, angular velocity and angular acceleration of hip and knee, respectively; τ ∈ R2 is a torque for the rehabilitation robot, which represents admissible control inputs; D(q) ∈ R2×2 is a positive-definite inertia matrix; C(q, q ) ∈ R2×2 is a centrifugal and Coriolis term; and G(q) ∈ R2 is related to gravity term
Summary
The number of limb impairment patients who were injured by stroke has increased year by year, and this disease has been developing in the direction of youth, seriously endangering the health of patients (Zorowitz et al, 2013). Conjugate gradient methods can be regarded as an effective optimization approach that utilizes an iteration point with a steep descent direction to generate conjugate direction and compute a global minimum point instead of solving linear equations of trust region-SQP algorithm (Sun et al, 2019). The studies on the rehabilitation training of lower-limb rehabilitation robot for MPC problem with projected active set conjugate gradient approach are scarce. The relationship of sEMG signals and motion intentions is established by an ESN model in section 5; passive and active rehabilitation training of lower-limb rehabilitation robot is illustrated and simulated by the proposed method, which is based on sEMG signals with ESN model and MPC problem.
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